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Theorem nvel 3917
 Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel ¬ V ∈ 𝐴

Proof of Theorem nvel
StepHypRef Expression
1 vprc 3916 . 2 ¬ V ∈ V
2 elex 2583 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 598 1 ¬ V ∈ 𝐴
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∈ wcel 1409  Vcvv 2574 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-13 1420  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038  ax-sep 3903 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by: (None)
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